Precisely.
I copped a ride to the ER once after a fall (I was pg). Even though I was totally ambulatory I wasn’t given a choice in the matter. Legal reasons and such I was told.
Not just that, I guess. A patient on a gurney is a complete unit of treatment. All his belongings are there; all the paperwork; all the IV, all the sensors. And it's all mobile, so the patient can be moved between stations - in a small surgery center, for example, from the admission nurse to the anesthesiologist, then to the operating room, then to the recovery room, then to release. If anything goes wrong the patient can be moved, on the same gurney, to a different specialist or to a different facility - regardless of whether the patient is awake or not (and that can change in an instant.)